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SOLVING NONLINEAR DYNAMIC TRANSPORT CONTROL PROBLLEMS BY USING BIONIC OPTIMIZATION TOOLS
Last modified: 2017-05-26
Abstract
ABSTRACT
Control of dynamic transport problems is a very common and well-studied class of tasks. Classical control theory covers successfully most of the questions posed. Nevertheless, in non-linear problems, the classical tools might be less efficient or even not well applicable. On the other hand, we can transform most of the control problems into optimization tasks, e.g. by minimizing deficits of the solutions found. In consequence, the option to replace the control problem by an optimization problem and use Bionic Optimization allows dealing with the given task even in the presence of strong nonlinearities and many optimization parameters.
Bionic Optimization, especially Evolutionary Strategies or Particle Swarm Optimization proves to be able to deal with non-trivial optimization challenges. The case of the presence of some or many local optima is not a real limitation to their ability to find good, very good or even best solutions. On the other hand, the non-uniqueness of the solutions found might be a challenge. We have to understand, whether differently appearing solutions are really different or if they belong to a family of solutions close to one equivalent good solution.
Today we understand that optimization of engineering problems should be done in conjunction with reliability and robustness studies. Best solutions found by advanced optimization strategies are of little interest, if they do not yield proposals that are well performing in real world situations. The inevitable scatter of optimization and other parameters must not produce final products, which do not work properly under service conditions. In consequence, we try to combine optimization, robustness and reliability studies into one integrated process.
The control of cranes is a common exampled used to demonstrate the performance of control strategies. A long rope connects a given payload and a driving system. After a certain travel history, the payload is to be placed at a given position with a predefined velocity. During the traveling and in a short time interval following the traveling, the driving system acts to perform additional positioning steps to satisfy the requirements of the transport and final position. For simple linear 1D crane problems there exist classical solutions, which we use to qualify the performance of newly proposed ideas.
In the case of 2D and 3D travels of the payload, including nonlinear effects the classical approaches are less applicable. The inherent non-linearity and long travel times require adapted studies, which do not converge after small numbers of iterations. Even when using highly elaborated Bionic Optimization strategies the total number of individual studies often becomes inacceptable. Therefor there exists a need to find methods to accelerate the processes and to develop fast ways to propose well performing solutions.
Some examples of 1D and 2D crane problems help to understand the questions posed and to outline the solutions we like to apply to the problems mentioned. We present advantages as well as difficult situations of the approaches used and discuss the benefits. Even when taking into account all the improvements, which we are able to make, it must not be disregarded that optimization is a time and computing power-consuming task as soon as there are higher numbers of free parameters. Adding reliability and robustness studies increases the total effort to find good solutions. Nevertheless, the use of advanced optimization tools helps in many cases to solve problems, which are difficult to handle without using these tools.
Control of dynamic transport problems is a very common and well-studied class of tasks. Classical control theory covers successfully most of the questions posed. Nevertheless, in non-linear problems, the classical tools might be less efficient or even not well applicable. On the other hand, we can transform most of the control problems into optimization tasks, e.g. by minimizing deficits of the solutions found. In consequence, the option to replace the control problem by an optimization problem and use Bionic Optimization allows dealing with the given task even in the presence of strong nonlinearities and many optimization parameters.
Bionic Optimization, especially Evolutionary Strategies or Particle Swarm Optimization proves to be able to deal with non-trivial optimization challenges. The case of the presence of some or many local optima is not a real limitation to their ability to find good, very good or even best solutions. On the other hand, the non-uniqueness of the solutions found might be a challenge. We have to understand, whether differently appearing solutions are really different or if they belong to a family of solutions close to one equivalent good solution.
Today we understand that optimization of engineering problems should be done in conjunction with reliability and robustness studies. Best solutions found by advanced optimization strategies are of little interest, if they do not yield proposals that are well performing in real world situations. The inevitable scatter of optimization and other parameters must not produce final products, which do not work properly under service conditions. In consequence, we try to combine optimization, robustness and reliability studies into one integrated process.
The control of cranes is a common exampled used to demonstrate the performance of control strategies. A long rope connects a given payload and a driving system. After a certain travel history, the payload is to be placed at a given position with a predefined velocity. During the traveling and in a short time interval following the traveling, the driving system acts to perform additional positioning steps to satisfy the requirements of the transport and final position. For simple linear 1D crane problems there exist classical solutions, which we use to qualify the performance of newly proposed ideas.
In the case of 2D and 3D travels of the payload, including nonlinear effects the classical approaches are less applicable. The inherent non-linearity and long travel times require adapted studies, which do not converge after small numbers of iterations. Even when using highly elaborated Bionic Optimization strategies the total number of individual studies often becomes inacceptable. Therefor there exists a need to find methods to accelerate the processes and to develop fast ways to propose well performing solutions.
Some examples of 1D and 2D crane problems help to understand the questions posed and to outline the solutions we like to apply to the problems mentioned. We present advantages as well as difficult situations of the approaches used and discuss the benefits. Even when taking into account all the improvements, which we are able to make, it must not be disregarded that optimization is a time and computing power-consuming task as soon as there are higher numbers of free parameters. Adding reliability and robustness studies increases the total effort to find good solutions. Nevertheless, the use of advanced optimization tools helps in many cases to solve problems, which are difficult to handle without using these tools.